Can you renounce acquired Japanese citizenship?

It's legally okay to say goodbye to your Japanese nationality

Yes. In fact, unlike many countries, the ability to renounce your Japanese citizenship and/or leave Japan is explicitly guaranteed by the Constitution of Japan:

第 {dai}22条 {jō}　何人も、 {nanibito mo,}公共の福祉に {kōtsū no fukushi ni}反しない限り、 {han shinai kagiri,}居住、移転及び {kyojū, iten oyobi}職業選択の自由 {shokugyō sentaku no jiyū}を有する。 {o yū suru.}
２　何人も、 {nanibito mo,}外国に移住し、 {gaikoku ni ijū shi,}又は国籍を離脱する {mata wa kokuseki o ridatsu suru}自由を侵されない。 {jiyū o okasarenai.}

Article 22: Every person shall have freedom to choose and change his residence and to choose his occupation to the extent that it does not interfere with the public welfare. 2) Freedom of all persons to move to a foreign country and to divest themselves of their nationality shall be inviolate.

The United Nations' Universal Declaration of Human Rights also says everybody should have this right:

Article 15.

1. Everyone has the right to a nationality.
2.  No one shall be arbitrarily deprived of his nationality nor denied the right to change his nationality.

While almost all democratic countries of the world have laws that allow for the renunciation of your citizenship, most of them do not have it written in their constitutions, and many of them have procedures that must be followed to renounce. Most of the time, these procedures and rules are for your own protection. For example, the United States forces you to be outside of the United States in order to renounce (except for the extremely rare case of a formally declared time of war), and will make it very, very hard for you to make yourself become stateless — though it is possible, as proven by Mike Gulgoski, who is currently destitute thanks to a poorly planned Bitcoin scheme and can't leave the country of Slovakia because he has no passport. They will also force you to go through a long process (about three embassy appointments) and pay a fee for the process, wait for many months, and then go through another process for taxes.

Japan is much easier, though, and has a simple form, the 国籍離脱届 {kokuseki ridatsu todoke} (nationality divestment form), that they can process fairly quickly at any embassy. Like other countries, the Japanese government will want to see proof that you possess another nationality. While of questionable practice from a Japanese Constitutional Law point of view, this is in the spirit of the U.N. Treaty on the Convention on the Reduction of Statelessness, 1961.

Besides the possession of another nationality, you will also need an official copy of your family register (戸籍謄本 {koseki tōhon}) and documentation that proves where you live (either domestic or foreign). Anything written in a foreign language will need to have a Japanese translation. Multiple copies of every document will need to be provided.

Renunciation applies only to yourself. Your children or spouse do not get renounced with you. Those not yet 15 years old must have permission from a parent or guardian. Yes, a sixteen year old can theoretically renounce their citizenship.

The only cases in the Nationality Law that are listed for the re-acquistion of Japanese nationality are for cases where a minor does not have their Japanese nationality reserved by their parents or, after a dual national reaches 22 years of age, is unable to be reached or reach Japan or its embassies (an example they list as an acceptable excuse is a natural disaster!) at the time of their deadline to make a Choice of Nationality (国籍選択の宣言 {kokusekisentaku no sengen}).

Thus, with the exception of that case, renunciation or loss of nationality should, like the United States, be considered irrevocable. That does not mean you can't obtain it (possibly again) via naturalization, but it's important to remember that naturalization is not a right, so there's no guarantee that you'll be accepted.

Note that people who renounce their Japanese citizenship, like people who acquire Japanese citizenship via naturalization, have their legal Japanese names published in the Diet (国会 {kokkai})'s Official Gazette (官報 {kampō}). On average, less than 150 Japanese renounce their Japanese citizenship per year.

I couldn't find an example of a person who lost their nationality via renunciation then reacquired it again via naturalization (in Japan or the United States).